A096031 - OEIS

%I #14 Jun 15 2020 21:08:34

%S 19,90,120,150,244,585,700,769,1414,1474,1909,2829,3030,4774,6154,

%T 6324,7804,8274,8455,10614,11544,11725,12195,13675,13845,15094,15225,

%U 16969,17170,18525,19230,19299,19755,19849,19879,47170,55165,90844,109155

%N Take pairs (a, b), sorted on a, such that T(a)+T(b)=concatenation of a and b, where T(k) is the k-th triangular number A000217(k). Sequence gives values of a.

%C For values of b see A096032.

%D J. S. Madachy, Madachy's Mathematical Recreations, pp. 166 Dover NY 1979.

%H Chai Wah Wu, <a href="/A096031/b096031.txt">Table of n, a(n) for n = 1..294</a>

%e 244 of the sequence forms a pair with 2196 and we indeed have T(244)+T(2196)=29890+2412306=2442196.

%t f[n_] := Block[{k = n + 1, t1 = n(n + 1)/2, td = IntegerDigits[n]}, While[k < 15*n && t1 + k(k + 1)/2 != FromDigits[ Join[ td, IntegerDigits[k]]], k++ ]; If[k != 15*n, k, 0]]; Do[ k = f[n]; If[k != 0, Print[n, " & ", k]], {n, 10^6}] (* _Robert G. Wilson v_, Jun 21 2004 *)

%K nonn,base

%O 1,1

%A _Lekraj Beedassy_, Jun 16 2004

%E Two more terms from _Robert G. Wilson v_, Jun 21 2004

%E Terms from a(19) onwards from _David Wasserman_, May 14 2007